Prime Numbers And Factorization

1) Which of the following numbers is not prime?

29

31

37

49

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The number 49 is not prime because it can be divided evenly by 1, 7, and 49 (7 x 7 = 49). In contrast, 29, 31, and 37 are prime numbers as they cannot be divided evenly by any other numbers except for 1 and themselves.

Explanation

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The number 49 is not prime because it can be divided evenly by 1, 7, and 49 (7 x 7 = 49). In contrast, 29, 31, and 37 are prime numbers as they cannot be divided evenly by any other numbers except for 1 and themselves.

2) How many prime numbers are between 20 and 40?

4

5

6

7

The number 7 has exactly two factors, 1 and 7, so the answer is 2 factors.

Explanation

The number 7 has exactly two factors, 1 and 7, so the answer is 2 factors.

3) Which of these is the prime factorization of 45?

3 × 15

5 × 9

3 × 3 × 5

45 × 1

The prime factorization of 45 is 3 × 3 × 5.

Explanation

The prime factorization of 45 is 3 × 3 × 5.

4) Which pair includes two prime numbers?

25 and 27

17 and 19

21 and 23

33 and 35

Both 17 and 19 are prime numbers.

Explanation

Both 17 and 19 are prime numbers.

5) What is the prime factorization of 60?

2 × 30

2 × 2 × 3 × 5

4 × 15 × 1

60 × 1

The prime factorization of 60 is 2 × 2 × 3 × 5.

Explanation

The prime factorization of 60 is 2 × 2 × 3 × 5.

6) What is the largest prime number less than 50?

47

49

45

43

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. The largest prime number less than 50 is 47, as it has no divisors other than 1 and itself.

Explanation

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. The largest prime number less than 50 is 47, as it has no divisors other than 1 and itself.

7) Which number is composite?

41

43

45

47

The number 45 is composite because 45 = 3 × 15.

Explanation

The number 45 is composite because 45 = 3 × 15.

8) Which number is a prime factor of 100?

20

25

5

50

The prime factors of 100 are 2 and 5, so 5 is correct.

Explanation

The prime factors of 100 are 2 and 5, so 5 is correct.

9) Which number is composite?

59

61

63

67

The number 63 is composite because 63 = 7 × 9.

Explanation

The number 63 is composite because 63 = 7 × 9.

10) Which number is a prime factor of 84?

6

3

21

14

A prime factor is a factor that is a prime number. The number 84 can be factored into prime factors as 2, 3, and 7. Among the given options, only 3 is a prime number and a factor of 84, making it the correct answer.

Explanation

A prime factor is a factor that is a prime number. The number 84 can be factored into prime factors as 2, 3, and 7. Among the given options, only 3 is a prime number and a factor of 84, making it the correct answer.

11) Which number is the smallest two-digit prime?

10

11

12

13

The smallest two-digit prime number is 11.

Explanation

The smallest two-digit prime number is 11.

12) How many prime factors are in the prime factorization of 90 counting repeats?

2

3

4

5

The number 90 has three prime factors: 2, 3, and 5.

Explanation

The number 90 has three prime factors: 2, 3, and 5.

13) Which number below is prime?

51

53

55

57

The number 53 is prime because its only factors are 1 and 53.

Explanation

The number 53 is prime because its only factors are 1 and 53.

14) Which of the following is a prime number greater than 70?

71

72

75

77

The number 71 is prime and greater than 70.

Explanation

The number 71 is prime and greater than 70.

15) Which number has exactly two factors?

49

51

53

55

The number 53 has exactly two factors, 1 and 53.

Explanation

The number 53 has exactly two factors, 1 and 53.

Prime Numbers and Factorization

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